# Modified logarithmic Sobolev inequalities for canonical ensembles

Abstract : In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential. These inequalities were introduced by Bobkov and Ledoux, and are closely related to concentration of measure and transport-entropy inequalities. Our method is an adaptation of the iterated two-scale approach that was developed by Menz and Otto to prove the usual logarithmic Sobolev inequality in this context. As a consequence, we obtain convergence in Wasserstein distance $W_p$ for Kawasaki dynamics on the Ginzburg-Landau model.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01874814
Contributor : Max Fathi <>
Submitted on : Friday, September 14, 2018 - 6:00:57 PM
Last modification on : Friday, March 27, 2020 - 3:01:40 AM

### Identifiers

• HAL Id : hal-01874814, version 1
• ARXIV : 1306.1484

### Citation

Max Fathi. Modified logarithmic Sobolev inequalities for canonical ensembles. ESAIM: Probability and Statistics, EDP Sciences, 2015. ⟨hal-01874814⟩

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